Properties of triangles, quadrilaterals and circles · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Properties of Parallelograms, Squares, and Circles

Mathematics · Geometry · ages 11-13
Name ______________________   Date ____________

  1. A circle has radius 5 cm. What is its diameter, in cm?

    Answer: ______________

  2. Which is ALWAYS true of a parallelogram?

    • Opposite sides are parallel and equal
    • All four angles are right angles
    • All four sides are equal
    • Diagonals are equal in length

  3. In a parallelogram, what is true about a pair of opposite angles?

    • They are always equal
    • They always add up to 180 degrees
    • They are always right angles

  4. The diameter of a circle is always twice its radius.

    Circle one:   True   False

  5. A rhombus has sides 7 cm. What is its perimeter, in cm?

    Answer: ______________

  6. A circle has a radius of 4 cm. What is its diameter, in cm?

    Answer: ______________

  7. The diagonals of a parallelogram always...

    • Are equal in length
    • Cross at right angles
    • Bisect each other
    • Are longer than the sides

  8. Max says a parallelogram's opposite angles are equal but its diagonals never cross in the middle. Is Max right?

    Circle one:   True   False

  9. A student says: 'If a shape's diagonals bisect each other, it must have four right angles.' What is wrong with this claim?

    • Diagonals bisecting each other only happens in triangles
    • Diagonals never bisect each other in a four-sided shape
    • Diagonals bisecting each other is true for parallelograms in general, not just ones with right angles

  10. Which statement links radius, diameter and circumference correctly?

    • Radius is twice the diameter; circumference equals diameter
    • Circumference is twice the radius; diameter equals pi
    • Diameter halves the radius; circumference is pi plus diameter
    • Diameter is twice the radius; circumference is pi times diameter
LightMySky · lightmysky.comW1-mt_DNYQLahbfa-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Properties of Parallelograms, Squares, and Circles W1-mt_DNYQLahbfa-s1

  1. 10 · Diameter is twice the radius: 2 x 5 = 10 cm.
  2. Opposite sides are parallel and equal · Parallel, equal opposite sides define the family; the rest suit only special members.
  3. They are always equal · Opposite angles in a parallelogram are always equal to each other.
  4. True · d = 2r for every circle, with no exceptions.
  5. 28 · Four equal sides of 7 cm give 4 x 7 = 28 cm.
  6. 8 · Diameter is always twice the radius: 2 times 4 is 8.
  7. Bisect each other · The diagonals always cut each other in half (bisect).
  8. False · Max is half right then wrong: opposite angles are equal AND diagonals bisect (cross centrally).
  9. Diagonals bisecting each other is true for parallelograms in general, not just ones with right angles · Every parallelogram has diagonals that bisect each other, including ones with slanted, non-right angles.
  10. Diameter is twice the radius; circumference is pi times diameter · Diameter doubles the radius, and circumference is pi diameters.
Worksheet · LightMySky